The style used in "The Rape of the Lock" is mock epic or, as Pope calls it in a subtitle, "An Heroi-Comical Poem." Pope treats these relatively trivial events as if they were wars and journeys characteristic of those in The Iliad and The Odyssey.
Pope explains at the beginning of Canto 1 that this will be an impressive description of a minor event:
What dire offense from amorous causes springs,
What mighty contests rise from trivial things,
I sing--This verse to Caryll, Muse! is due:
This, even Belinda may vouchsafe to view:
Slight is the subject, but not so the praise, (1.1-5)
Pope was asked to write this to settle a quarrel between two families but it became more of a satire on the vanity of aristocrats and the upper class. This poem is somewhat in the style of "burlesque," which is when trivial subjects are elevated to levels of supreme significance. The tragic "event" in the poem is when Lord Petre clips a lock of Belinda's hair. Note the epic language which describes this trivial event:
Steel could the labor of the Gods destroy,
And strike to dust the imperial powers of Troy;
Steel could the woks of mortal pride confound,
And hew triumphal arches to the ground.
What wonder then, fair nymph! thy hairs should feel,
The conquering force of unresisted steel? (3.173-178)
Also in epic style, there are supernatural forces involved. Just as Odysseus is helped and hurt by different gods such as Athena, Belinda is surrounded by sprites and sylphs. Ariel, a sprite, tries to warn Belinda about pride and to be wary of men. Sylphs are brought to help guard Belinda. She ignores both warnings and does not see the attack (cutting of the lock) coming. In epic poems, gods become involved because these poems are about wars and journeys which will affect history. The satire here makes it seem ridiculous that gods would trouble themselves with a vain woman who may or may not lose a lock of hair at a tea party.
"The Rape of the Lock" is written in heroic couplets. In keeping with the lofty and epic style, it has all the appearances of a serious epic but the subject matter is about the trivial lives of these superficial people.